Hands On Exercise 6.1 -

Author

Allan Chong

Overview

Water is a crucial resource for humanity. People must have access to clean water in order to be healthy. It promotes a healthy environment, peace and security, and a sustainable economy. However, more than 40% of the world’s population lacks access to enough clean water. According to UN-Water, 1.8 billion people would live in places with a complete water shortage by 2025. One of the many areas that the water problem gravely threatens is food security. Agriculture uses over 70% of the freshwater that is present on Earth.

The severe water shortages and water quality issues are seen in underdeveloped countries. Up to 80% of infections in developing nations are attributed to inadequate water and sanitation infrastructure.

Despite technological advancement, providing rural people with clean water continues to be a key development concern in many countries around the world, especially in those on the continent of Africa.

We will attempt to conduct logistic regression of the Osun state in Nigeria with the water points attributes in this exercise.

Data points of interest

In this assignment, we will attempt to regionalize Nigeria based on the following variables:

  • Functional status,

  • distance_to_primary_road

  • distance_to_secondary_road

  • distance_to_city

  • distance_to_town

  • water_point_population

  • local_population_1km

  • usage_capacity

  • is_urban

  • water_source_clean

Getting Started

First, we load the required packages in R

  • Spatial data handling & Clustering

    • sf, spdep
  • Choropleth mapping

    • tmap
  • Attribute data handling

    • tidyverse especially readr, ggplot2 and dplyr and funModeling
  • Exploration Data visualization and analysis

    • corrplot, ggpubr, GGally, knitr and skimr
  • Logistic Regression

    • blorr, caret, GWModel
pacman::p_load(knitr, spdep, tmap, sf, 
               ggpubr, GGally, funModeling,
               corrplot, GWmodel,
               tidyverse, blorr, skimr, caret)

Spatial Data

First we load the Osun spatial features using readRDS()

osun = readRDS("data/rds/Osun.rds")

Aspatial Data

Next we load the Osun water point data using readRDS()

osun_wpt_sf = readRDS("data/rds/Osun_wp_sf.rds")

freq(data=osun_wpt_sf, input = 'status')

  status frequency percentage cumulative_perc
1   TRUE      2642       55.5            55.5
2  FALSE      2118       44.5           100.0

We toggle the mode to interactive mode by using ttm() and plot the map using functions from the tmap package

ttm()
tm_shape(osun) +
tm_polygons(alpha = 0.4) + 
  tm_shape(osun_wpt_sf) +
  tm_dots(col="status")

Exploratory Data Analysis

Using the skimr package, we can give a brief summary statistics of the variables found in the osun_wpt_sf data frame.

osun_wpt_sf %>%
  skim()
Data summary
Name Piped data
Number of rows 4760
Number of columns 75
_______________________
Column type frequency:
character 47
logical 5
numeric 23
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
source 0 1.00 5 44 0 2 0
report_date 0 1.00 22 22 0 42 0
status_id 0 1.00 2 7 0 3 0
water_source_clean 0 1.00 8 22 0 3 0
water_source_category 0 1.00 4 6 0 2 0
water_tech_clean 24 0.99 9 23 0 3 0
water_tech_category 24 0.99 9 15 0 2 0
facility_type 0 1.00 8 8 0 1 0
clean_country_name 0 1.00 7 7 0 1 0
clean_adm1 0 1.00 3 5 0 5 0
clean_adm2 0 1.00 3 14 0 35 0
clean_adm3 4760 0.00 NA NA 0 0 0
clean_adm4 4760 0.00 NA NA 0 0 0
installer 4760 0.00 NA NA 0 0 0
management_clean 1573 0.67 5 37 0 7 0
status_clean 0 1.00 9 32 0 7 0
pay 0 1.00 2 39 0 7 0
fecal_coliform_presence 4760 0.00 NA NA 0 0 0
subjective_quality 0 1.00 18 20 0 4 0
activity_id 4757 0.00 36 36 0 3 0
scheme_id 4760 0.00 NA NA 0 0 0
wpdx_id 0 1.00 12 12 0 4760 0
notes 0 1.00 2 96 0 3502 0
orig_lnk 4757 0.00 84 84 0 1 0
photo_lnk 41 0.99 84 84 0 4719 0
country_id 0 1.00 2 2 0 1 0
data_lnk 0 1.00 79 96 0 2 0
water_point_history 0 1.00 142 834 0 4750 0
clean_country_id 0 1.00 3 3 0 1 0
country_name 0 1.00 7 7 0 1 0
water_source 0 1.00 8 30 0 4 0
water_tech 0 1.00 5 37 0 20 0
adm2 0 1.00 3 14 0 33 0
adm3 4760 0.00 NA NA 0 0 0
management 1573 0.67 5 47 0 7 0
adm1 0 1.00 4 5 0 4 0
New Georeferenced Column 0 1.00 16 35 0 4760 0
lat_lon_deg 0 1.00 13 32 0 4760 0
public_data_source 0 1.00 84 102 0 2 0
converted 0 1.00 53 53 0 1 0
created_timestamp 0 1.00 22 22 0 2 0
updated_timestamp 0 1.00 22 22 0 2 0
Geometry 0 1.00 33 37 0 4760 0
ADM2_EN 0 1.00 3 14 0 30 0
ADM2_PCODE 0 1.00 8 8 0 30 0
ADM1_EN 0 1.00 4 4 0 1 0
ADM1_PCODE 0 1.00 5 5 0 1 0

Variable type: logical

skim_variable n_missing complete_rate mean count
rehab_year 4760 0 NaN :
rehabilitator 4760 0 NaN :
is_urban 0 1 0.39 FAL: 2884, TRU: 1876
latest_record 0 1 1.00 TRU: 4760
status 0 1 0.56 TRU: 2642, FAL: 2118

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
row_id 0 1.00 68550.48 10216.94 49601.00 66874.75 68244.50 69562.25 471319.00 ▇▁▁▁▁
lat_deg 0 1.00 7.68 0.22 7.06 7.51 7.71 7.88 8.06 ▁▂▇▇▇
lon_deg 0 1.00 4.54 0.21 4.08 4.36 4.56 4.71 5.06 ▃▆▇▇▂
install_year 1144 0.76 2008.63 6.04 1917.00 2006.00 2010.00 2013.00 2015.00 ▁▁▁▁▇
fecal_coliform_value 4760 0.00 NaN NA NA NA NA NA NA
distance_to_primary_road 0 1.00 5021.53 5648.34 0.01 719.36 2972.78 7314.73 26909.86 ▇▂▁▁▁
distance_to_secondary_road 0 1.00 3750.47 3938.63 0.15 460.90 2554.25 5791.94 19559.48 ▇▃▁▁▁
distance_to_tertiary_road 0 1.00 1259.28 1680.04 0.02 121.25 521.77 1834.42 10966.27 ▇▂▁▁▁
distance_to_city 0 1.00 16663.99 10960.82 53.05 7930.75 15030.41 24255.75 47934.34 ▇▇▆▃▁
distance_to_town 0 1.00 16726.59 12452.65 30.00 6876.92 12204.53 27739.46 44020.64 ▇▅▃▃▂
rehab_priority 2654 0.44 489.33 1658.81 0.00 7.00 91.50 376.25 29697.00 ▇▁▁▁▁
water_point_population 4 1.00 513.58 1458.92 0.00 14.00 119.00 433.25 29697.00 ▇▁▁▁▁
local_population_1km 4 1.00 2727.16 4189.46 0.00 176.00 1032.00 3717.00 36118.00 ▇▁▁▁▁
crucialness_score 798 0.83 0.26 0.28 0.00 0.07 0.15 0.35 1.00 ▇▃▁▁▁
pressure_score 798 0.83 1.46 4.16 0.00 0.12 0.41 1.24 93.69 ▇▁▁▁▁
usage_capacity 0 1.00 560.74 338.46 300.00 300.00 300.00 1000.00 1000.00 ▇▁▁▁▅
days_since_report 0 1.00 2692.69 41.92 1483.00 2688.00 2693.00 2700.00 4645.00 ▁▇▁▁▁
staleness_score 0 1.00 42.80 0.58 23.13 42.70 42.79 42.86 62.66 ▁▁▇▁▁
location_id 0 1.00 235865.49 6657.60 23741.00 230638.75 236199.50 240061.25 267454.00 ▁▁▁▁▇
cluster_size 0 1.00 1.05 0.25 1.00 1.00 1.00 1.00 4.00 ▇▁▁▁▁
lat_deg_original 4760 0.00 NaN NA NA NA NA NA NA
lon_deg_original 4760 0.00 NaN NA NA NA NA NA NA
count 0 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 ▁▁▇▁▁
osun_wpt_sf_clean = osun_wpt_sf %>% #filter the required fields
  filter_at(vars(status,
                 distance_to_primary_road,
                 distance_to_secondary_road,
                 distance_to_city,
                 distance_to_town,
                 water_point_population,
                 local_population_1km,
                 usage_capacity,
                 is_urban,
                 water_source_clean),
            all_vars(!is.na(.))) %>% #remove the na variable
            mutate(usage_capacity = as.factor(usage_capacity) 
                   #change it to factors as there are only 3 factors, 300, 500 and 1000
            )
var_list = c("water_source_clean",
                 "distance_to_primary_road",
                 "distance_to_secondary_road",
                 "distance_to_tertiary_road",
                 "distance_to_city",
                 "distance_to_town",
                 "water_point_population",
                 "local_population_1km",
                 "usage_capacity",
                 "is_urban",
                 "status"
                 )

osun_wp = osun_wpt_sf_clean %>%
  select(var_list)  %>%
  st_set_geometry(NULL)
cluster_vars.cor = cor(osun_wp[,2:7]) 

corrplot.mixed(cluster_vars.cor, 
               lower = "ellipse", 
               upper = "number", 
               tl.pos = "lt", 
               diag="l", 
               tl.col="black")

According to Calkins (2005), variables that can be regarded as having a high degree of correlation are indicated by correlation coefficients with magnitudes between ± 0.7 and 1.0. Hence we conclude that there is no highly correlated variables.

Multilogistic Regression

#status is the variable we are interested as y
model = glm(status ~ distance_to_primary_road + distance_to_secondary_road + 
              distance_to_tertiary_road + distance_to_city + 
              distance_to_town + is_urban + usage_capacity +
              water_source_clean + water_point_population + local_population_1km,
            data = osun_wpt_sf_clean,
            family = binomial(link = 'logit'))

Instead of using a typical R Report, we use blr_regress() to convert the modelling result into a report

blr_regress(model)
                             Model Overview                              
------------------------------------------------------------------------
Data Set    Resp Var    Obs.    Df. Model    Df. Residual    Convergence 
------------------------------------------------------------------------
  data       status     4756      4755           4744           TRUE     
------------------------------------------------------------------------

                    Response Summary                     
--------------------------------------------------------
Outcome        Frequency        Outcome        Frequency 
--------------------------------------------------------
   0             2114              1             2642    
--------------------------------------------------------

                                 Maximum Likelihood Estimates                                   
-----------------------------------------------------------------------------------------------
               Parameter                    DF    Estimate    Std. Error    z value     Pr(>|z|) 
-----------------------------------------------------------------------------------------------
              (Intercept)                   1      0.3887        0.1124      3.4588       5e-04 
        distance_to_primary_road            1      0.0000        0.0000     -0.7153      0.4744 
       distance_to_secondary_road           1      0.0000        0.0000     -0.5530      0.5802 
       distance_to_tertiary_road            1      1e-04         0.0000      4.6708      0.0000 
            distance_to_city                1      0.0000        0.0000     -4.7574      0.0000 
            distance_to_town                1      0.0000        0.0000     -4.9170      0.0000 
              is_urbanTRUE                  1     -0.2971        0.0819     -3.6294       3e-04 
           usage_capacity1000               1     -0.6230        0.0697     -8.9366      0.0000 
water_source_cleanProtected Shallow Well    1      0.5040        0.0857      5.8783      0.0000 
   water_source_cleanProtected Spring       1      1.2882        0.4388      2.9359      0.0033 
         water_point_population             1      -5e-04        0.0000    -11.3686      0.0000 
          local_population_1km              1      3e-04         0.0000     19.2953      0.0000 
-----------------------------------------------------------------------------------------------

 Association of Predicted Probabilities and Observed Responses  
---------------------------------------------------------------
% Concordant          0.7347          Somers' D        0.4693   
% Discordant          0.2653          Gamma            0.4693   
% Tied                0.0000          Tau-a            0.2318   
Pairs                5585188          c                0.7347   
---------------------------------------------------------------

We will exclude distance_to_primary_road & distance_to_secondary_road as they have a p value of > 0.05 implying that they are not statistically significant

Interpret the variables by below rules:

For categorical variable, a +ve value implies an above avg correlation and a -ve value implies a below avg correlation

For continuous variables, +ve value implies a direct correlation and a -ve correlation implies an inverse correlation

Only do the above when they are statistically significant

blr_confusion_matrix(model, cutoff = 0.5)
Confusion Matrix and Statistics 

          Reference
Prediction FALSE TRUE
         0  1301  738
         1   813 1904

                Accuracy : 0.6739 
     No Information Rate : 0.4445 

                   Kappa : 0.3373 

McNemars's Test P-Value  : 0.0602 

             Sensitivity : 0.7207 
             Specificity : 0.6154 
          Pos Pred Value : 0.7008 
          Neg Pred Value : 0.6381 
              Prevalence : 0.5555 
          Detection Rate : 0.4003 
    Detection Prevalence : 0.5713 
       Balanced Accuracy : 0.6680 
               Precision : 0.7008 
                  Recall : 0.7207 

        'Positive' Class : 1

Using Geographically Weighted Logistic Regression (GWLR)

First We must first transform osun_wp_sf_clean into a spatial polygons data frame using as_Spatial(). This is because only SP objects (SpatialPointDataFrame) is required to generate the GWLR

osun_wp_sp = osun_wpt_sf_clean %>%
  select(var_list)  %>%
  as_Spatial()

Using a fixed distance matrix

bw.fixed = bw.ggwr(status ~ distance_to_primary_road + distance_to_secondary_road + 
              distance_to_tertiary_road + distance_to_city + 
              distance_to_town + is_urban + usage_capacity +
              water_source_clean + water_point_population + local_population_1km,
              data = osun_wp_sp,
              family = "binomial",
              approach = "AIC",
              kernel = "gaussian",
              adaptive = FALSE,
              longlat = FALSE #use false if its converted into projected coord system (number will be very big)
              
              )
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
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2597.255m ~ 2.6km

gwlr.fixed = ggwr.basic(status ~ distance_to_primary_road + distance_to_secondary_road + 
              distance_to_tertiary_road + distance_to_city + 
              distance_to_town + is_urban + usage_capacity +
              water_source_clean + water_point_population + local_population_1km,
              data = osun_wp_sp,
              bw = bw.fixed,
              family = "binomial",
              kernel = "gaussian",
              adaptive = FALSE,
              longlat = FALSE #use false if its converted into projected coord system (number will be very big)
)
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gwlr.fixed
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2022-12-17 13:30:14 
   Call:
   ggwr.basic(formula = status ~ distance_to_primary_road + distance_to_secondary_road + 
    distance_to_tertiary_road + distance_to_city + distance_to_town + 
    is_urban + usage_capacity + water_source_clean + water_point_population + 
    local_population_1km, data = osun_wp_sp, bw = bw.fixed, family = "binomial", 
    kernel = "gaussian", adaptive = FALSE, longlat = FALSE)

   Dependent (y) variable:  status
   Independent variables:  distance_to_primary_road distance_to_secondary_road distance_to_tertiary_road distance_to_city distance_to_town is_urban usage_capacity water_source_clean water_point_population local_population_1km
   Number of data points: 4756
   Used family: binomial
   ***********************************************************************
   *              Results of Generalized linear Regression               *
   ***********************************************************************

Call:
NULL

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-124.555    -1.755     1.072     1.742    34.333  

Coefficients:
                                           Estimate Std. Error z value Pr(>|z|)
Intercept                                 3.887e-01  1.124e-01   3.459 0.000543
distance_to_primary_road                 -4.642e-06  6.490e-06  -0.715 0.474422
distance_to_secondary_road               -5.143e-06  9.299e-06  -0.553 0.580230
distance_to_tertiary_road                 9.683e-05  2.073e-05   4.671 3.00e-06
distance_to_city                         -1.686e-05  3.544e-06  -4.757 1.96e-06
distance_to_town                         -1.480e-05  3.009e-06  -4.917 8.79e-07
is_urbanTRUE                             -2.971e-01  8.185e-02  -3.629 0.000284
usage_capacity1000                       -6.230e-01  6.972e-02  -8.937  < 2e-16
water_source_cleanProtected Shallow Well  5.040e-01  8.574e-02   5.878 4.14e-09
water_source_cleanProtected Spring        1.288e+00  4.388e-01   2.936 0.003325
water_point_population                   -5.097e-04  4.484e-05 -11.369  < 2e-16
local_population_1km                      3.451e-04  1.788e-05  19.295  < 2e-16
                                            
Intercept                                ***
distance_to_primary_road                    
distance_to_secondary_road                  
distance_to_tertiary_road                ***
distance_to_city                         ***
distance_to_town                         ***
is_urbanTRUE                             ***
usage_capacity1000                       ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring       ** 
water_point_population                   ***
local_population_1km                     ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6534.5  on 4755  degrees of freedom
Residual deviance: 5688.0  on 4744  degrees of freedom
AIC: 5712

Number of Fisher Scoring iterations: 5


 AICc:  5712.099
 Pseudo R-square value:  0.1295351
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 2599.672 
   Regression points: the same locations as observations are used.
   Distance metric: A distance matrix is specified for this model calibration.

   ************Summary of Generalized GWR coefficient estimates:**********
                                                   Min.     1st Qu.      Median
   Intercept                                -8.7228e+02 -4.9955e+00  1.7600e+00
   distance_to_primary_road                 -1.9389e-02 -4.8031e-04  2.9618e-05
   distance_to_secondary_road               -1.5921e-02 -3.7551e-04  1.2317e-04
   distance_to_tertiary_road                -1.5618e-02 -4.2368e-04  7.6179e-05
   distance_to_city                         -1.8416e-02 -5.6217e-04 -1.2726e-04
   distance_to_town                         -2.2411e-02 -5.7283e-04 -1.5155e-04
   is_urbanTRUE                             -1.9790e+02 -4.2908e+00 -1.6864e+00
   usage_capacity1000                       -2.0772e+01 -9.7231e-01 -4.1592e-01
   water_source_cleanProtected.Shallow.Well -2.0789e+01 -4.5190e-01  5.3340e-01
   water_source_cleanProtected.Spring       -5.2235e+02 -5.5977e+00  2.5441e+00
   water_point_population                   -5.2208e-02 -2.2767e-03 -9.8875e-04
   local_population_1km                     -1.2698e-01  4.9952e-04  1.0638e-03
                                                3rd Qu.      Max.
   Intercept                                 1.2763e+01 1073.2154
   distance_to_primary_road                  4.8443e-04    0.0142
   distance_to_secondary_road                6.0692e-04    0.0258
   distance_to_tertiary_road                 6.6814e-04    0.0128
   distance_to_city                          2.3718e-04    0.0150
   distance_to_town                          1.9271e-04    0.0224
   is_urbanTRUE                              1.2841e+00  744.3097
   usage_capacity1000                        3.0322e-01    5.9281
   water_source_cleanProtected.Shallow.Well  1.7849e+00   67.6343
   water_source_cleanProtected.Spring        6.7663e+00  317.4123
   water_point_population                    5.0102e-04    0.1309
   local_population_1km                      1.8157e-03    0.0392
   ************************Diagnostic information*************************
   Number of data points: 4756 
   GW Deviance: 2795.084 
   AIC : 4414.606 
   AICc : 4747.423 
   Pseudo R-square value:  0.5722559 

   ***********************************************************************
   Program stops at: 2022-12-17 13:30:46 

The AIC value of Geographically Weighted Regression (GWR) is 4414.606 vs Generalized Linear Regression (GLR) is 5712. Hence, we can conclude that there is a significant improvement on the GWR model

Note: Logistic regression does not have AICC

To assess the performance of gwLR, we need to first convert the SDF object as a data frame

gwr.fixed = as.data.frame(gwlr.fixed$SDF)

Next, we will label yhat values greater or equal to 0.5 into 1 and 0 otherwise. The result of the logical comparison will be saved into a new field call most

gwr.fixed = gwr.fixed %>% 
            mutate(most = 
                     ifelse(gwr.fixed$yhat >= 0.5, T, F))
gwr.fixed$y = as.factor(gwr.fixed$y)
gwr.fixed$most = as.factor(gwr.fixed$most)

cm = confusionMatrix(data = gwr.fixed$most, 
                      reference = gwr.fixed$y)
cm
Confusion Matrix and Statistics

          Reference
Prediction FALSE TRUE
     FALSE  1824  263
     TRUE    290 2379
                                          
               Accuracy : 0.8837          
                 95% CI : (0.8743, 0.8927)
    No Information Rate : 0.5555          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.7642          
                                          
 Mcnemar's Test P-Value : 0.2689          
                                          
            Sensitivity : 0.8628          
            Specificity : 0.9005          
         Pos Pred Value : 0.8740          
         Neg Pred Value : 0.8913          
             Prevalence : 0.4445          
         Detection Rate : 0.3835          
   Detection Prevalence : 0.4388          
      Balanced Accuracy : 0.8816          
                                          
       'Positive' Class : FALSE           
                                          

Perf increase from MLogR to 88.37% GWLR

Sensitivity increase from

Specificity increased from

Should apply localized strategy instead of using global localized strategy in order to identify reasons of non functional water points

Exclude the 2 statistically significant variables and run one more time..

osun_wpt_sf_selected = osun_wpt_sf_clean %>%
  select(c(ADM2_EN, ADM2_PCODE, ADM1_EN, ADM1_PCODE, status))

gwr_sf.fixed = cbind(osun_wpt_sf_selected, gwr.fixed)

prob_t = tm_shape(osun) + 
  tm_polygons(alpha = 0.1) +
  tm_shape(gwr_sf.fixed) +
  tm_dots(col="yhat",
  border.col = "gray60",
  border.lwd = 1) +
  tm_view(set.zoom.limits = c(8,14))

prob_t

References

Calkins K. G (2005) Applied Statistics - Lesson 5, Correlation Coefficients

https://www.andrews.edu/~calkins/math/edrm611/edrm05.htm#:~:text=Correlation%20coefficients%20whose%20magnitude%20are,can%20be%20considered%20highly%20correlated.